Friday, March 28, 2014

Non-sentences

Consider:

Many a philosopher was celebrated during his life. His work was culturally influential. And then after he died, he was all but forgotten.

Notice that "His work was culturally influential" has the grammatical form of a sentence, but is not a sentence. It is an open formula with "His" being a free variable, bound ultimately by the "Many a philosopher" quantifier. But there seem to be other contexts in which "His work was culturally influential" seems to be a sentence:

Bergson was celebrated during his life. His work was culturally influential. And then after he died, he was all but forgotten.

So it seems whether something is a sentence is sometimes contextually determined.

Maybe we can say that "his" is actually two words: one word functions as a variable and the other as a name (with reference anaphorically coming from another name). But on grounds of Ockham's razor this seems a poor move.

There is another move one can make here that seems better: The third-person pronoun is always a variable. In (1), it is bound by the "Many a philosopher" quantifier. In (2), it is bound by the "Bergson" quantifier. (Here I am following Montague's insight that names can be seen as functioning as quantifiers.)

Note added later: I think the name-as-variable move doesn't get one out of the contextuality of what's a sentence. Suppose that after I said (2), you said: "He is still quite influential." What you said is clearly a genuine sentence.

One could argue that neither instance of 'his work was culturally influential' is a sentence*, and that we should represent context as a variable assignment. Then in (2), the impression of sentencehood comes about because context forces us to interpret it relative to a variable assignment that maps 5 to Bergson.

(2) [he]5 ['s work] was culturally influential.

* In the sense that you're using the term---a closed wff? Speaking as a linguist, to hear 'x has the grammatical form of a sentence, but is not a sentence' sounds bizarre.

Even if we think of it in terms of context, there is still a difference. Context+(2) makes for a closed wff, while context+(1) does not make for one.

(To be honest, I am dubious of the distinction between context and utterance. Think of an encoding of English where you speak by making a tongue click, and your speech is decoded by taking the exact time in seconds of your click, converting it to binary, and taking the first 4096 bits after the binary point to be an ASCII encoding of what you said. Normally we think of the time of utterance as context, which would reduce the utterance to just a click. But that's clearly mistaken: all the grammatical structure is in the context here. In general, I think context has grammatical structure, albeit one we can't analyze very well.)

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I am a philosopher at Baylor University. This blog, however, does not purport to express in any way the opinions of Baylor University. Amateur science and technology work should not be taken to be approved by Baylor University. Use all information at your own risk.